Chapter 8.4, Problem 47STP

To determine

To calculate the number of different combinations of two courses possible for Kaila

Answer to Problem 47STP

For Kaila 15 different combinations of 2 courses are possible. The correct answer is option C.

Explanation of Solution

Given information:

There are total 6 courses in the music department and Kaila must choose exactly 2 of them and also she can choose any of the two courses out of 6 as there is no restriction

The given options are,

A.48

B.18

C.15

D.12

The order does not matter then choose 2 out of 6 possibilities. This can be represented as,

  $6C_2=\frac{6!}{2!\left(6-2\right)!}=\frac{6\times 5\times 4!}{2!\times 4!}=\frac{30}{2}=15$

Therefore, 15 different combinations of 2 courses are possible for Kaila.